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$\int \sqrt{x^{2} + 3 x} dx$ is equal to

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2x+32x2+3x−94log⁡2x+32+x2+3x∣+C

2x+34x2+3x−94log⁡2x+32+x2+3x∣+C

x+32x2+3x−98log⁡x+32+x2+3x∣+C

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detailed solution

Correct option is D

LetI=∫x2+3xdx=∫x2+3x−322+322dx=∫x+322−322dxI=x+322x+322−322−94×2log⁡x+32+x2+3x∣+C∵∫x2−a2dx=x2x2−a2−a22log⁡x+x2−a2⇒I=2x+34x2+3x−98log⁡2x+32+x2+3x+C

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∫x2+3xdx is equal to

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$\int \sqrt{x^{2} + 3 x} dx$ is equal to